Fuzzy confidence interval for fuzzy process capability index

Abstract

Process capability indices are used to determine whether a production process is capable of producing items within specification tolerance. In practice these indices are estimated using sample data, often with quite small sample sizes. Thus, it is of interest to obtain confidence limits for capability index given a sample estimate. Most of the traditional methods for assessing the capability of manufacturing processes are dealing with crisp quality. In this paper we obtain 100(1 − α)% fuzzy confidence interval for � $_p$ fuzzy process capability index, where instead of precise quality we have two membership functions for specification limits. We present several interpretations for introduced fuzzy confidence interval. Some numerical examples are given to clarify the method.